6 papers
Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
Giulio Ciraolo, Rosario Corso, Alberto Roncoroni
We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the t…
Serrin's type problems in warped product manifolds
Alberto Farina, Alberto Roncoroni
In this paper we consider Serrin's overdetermined problems in warped product manifolds and we prove Serrin's type rigidity results by using the P-function approach introduced by We…
Symmetry results for critical anisotropic -Laplacian equations in convex cones
Giulio Ciraolo, Alessio Figalli, Alberto Roncoroni
Given and , we consider the critical -Laplacian equation , which corresponds to critical points of the Sobolev inequality. Exploiting the…
On the umbilic set of immersed surfaces in three-dimensional space forms
Giovanni Catino, Alberto Roncoroni, Luigi Vezzoni
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a -dimensional space form has positive measure. In case of an im…
Quantitative stability for hypersurfaces with almost constant curvature in space forms
Giulio Ciraolo, Alberto Roncoroni, Luigi Vezzoni
The Alexandrov Soap Bubble Theorem asserts that the distance spheres are the only embedded closed connected hypersurfaces in space forms having constant mean curvature. The theorem…
The method of moving planes: a quantitative approach
Giulio Ciraolo, Alberto Roncoroni
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's over…